What is the difference? Would the NPC be limited to that storyline, whereas the DM's PC could move on to another story?

The difference is the difference between a PC and an NPC. A PC is a character that is the way a player views the world, through his eyes. An NPC is just one of many characters that a DM is in charge of. The game is about the PCs, an NPC even a permanent party member should never be equal to the PCs in game time and events.

Are you asking because you are the DM and want to have your own character in a game? Or are you a player who's DM wants to?

Would it be a faux pas for a DM to also play a PC in the same game? I suppose it could garner the DMs PC an advantage.

DMPCs, as such characters are called, have a bad reputation. It's very difficult for a DM to "properly" play such a character or even notice if they're not playing them "properly". The reputation is made even worse because some DMs have been abusive with said DMPCs, having them overshadow the PCs, and so the players are "anti-charmed" and see everything said DMPC does in the worst possible light (even if the DM in question isn't being abusive).

One time I introduced a DMPC in my d20 Modern game (set in Ancient China). The PCs needed a doctor badly, as we only had two to three players at a time. Instead of directly controlling the doctor NPC, I let them build him. He used the Ordinary class rules rather than the PC class rules (if you play 4e, picture said NPC as a "companion" rather than a full-fledged PC) and was two levels lower than the PCs to boot.

I had the players design and control him, so I couldn't accidentally make him better or worse at various things. Naturally, they tried to keep him out of trouble, but close enough that he couldn't get murdered when they looked the other way. In one session, they stormed a bandit hideout, and told him to hide behind a pillar and shoot arrows at the bad guys. Unfortunately, the bandits figured something like this would happen (I had the traps set up before the PCs announced their plans) and the doctor had a bunch of logs fall on his head. He lived though! Had I been playing the doctor, I don't know if that would have happened. (Would I have put him there anyway, hoping to scare the PCs by dropping logs on him? Or would I have had him avoid that area for whatever reason? Unfortunately, analyzing one's own thinking is not easy, as there's always subconscious influences.)

Sure you're allowed to be in charge of an extra body in the group. There have been times, as a DM , where I was in charge of an easy dozen or so extra bodies in the party. But the inherent dangers are in playing those characters as lead roles, instead of bit parts.

In D&D, it is literally impossible for you to run a game and experience it as a player at the same time. You should not even try to do so. Your players will not appreciate it, and you will not get anywhere near the same experience as you would as an actual player.

The dynamic between DM and players is one of the central features of RPGs. If you're running a PC, you're trying to be on both sides of the fence and throwing that dynamic out of whack.

NPCs are fine, as are henchmen, companions, etc, though I'd largely keep them as "guest stars" so to speak rather than permanent features of the party. The key is that they are not YOUR character. They are a character in the game. The players are still in the driver's seat.

A long (long) time ago I was in one with rotating DMs in a shared world (switched off every adventure or so), where whoever was DMing at the time had their character continue along with the party. I want to say they were usually treated the way a lot of games I'm in treat the PC of an absent player (sleep walking in the back until they're really needed for something only they can handle).

I've been in several where the DM provided a party-member NPC to fill in a void (no cleric or no thief). The key there was that they were a background supporting character (in spite of level and powers) and never in a lead or starring role. In some cases where I've run them I've let the party handle them most of the time in terms of actions and dice rolling when needed.

If you are lacking for bodies, try giving the players control of the extra characters who are going to be a key fixture of the groups encounters. It gets the players more involved, and lets them try out different things if something isn't quite working for them. They can take turns or double up depending on how many you need.

For characters who are not permanent party members, an NPC is more than fine.

If "A" is broken, that isn't a valid reason for "B" to be so, even if they vary in degree.

Tactician style Gamer, or so I have been told.

"Common sense is the collection of prejudices acquired by age eighteen."-Albert Einstein

Would it be a faux pas for a DM to also play a PC in the same game? I suppose it could garner the DMs PC an advantage.

People here don't like it. People here complain about a lot of social problems in D&D that I've never seen in real life (from smelly gamers to killer DM's to players who tell other players what to do). Like Steven Colbert talking about race, I assume it's real because people tell me about it, but I don't see it.

My experience with the DMPC is that it's fine.

The first campaign I played in was just the DM, his little brother, and me -- us two players never having played before. It made sense for the DM to create and manage some of the characters, and we never did file a union grievance about DMPC's takin' our jobs. So it always seemed natural to me.

The main complaints seem to be:

1) DMPC's are unfair. DM's will use their inside knowledge of the campaign and overwhelming stat and treasure advantages to boss us around and do all the cool stuff. Their characters will be super strong and we'll just be BMX Bandits to the DM's Angel Summoner, or Pippin and Merry to his Gandalf.

The way to solve this, shockingly, is for the DM to be a good DM. If he can design balanced NPCs in the campaign setting, and role play them with in-character knowledge only, he should be able to run an NPC party member.

If a DM can't handle running one party-member NPC that way, how can he "be trusted" to run the non-party NPC's and monster?

Surely the bartender in the tavern where your party just met each other is an NPC -- but he's run by the DM, so he might be the dreaded DMPC! Maybe the DM is planning to have him boss you around and be super powerful -- you'd better just tear up your character sheet and stomp off at the first sign of an NPC who might have a NAME -- too dangerous!

The other issue here is in how you treat the game. I've always seen D&D as a cooperative game where the team is working together to defeat a challenge. It doesn't make me mad when another player does something successfully, and I don't feel any different about an NPC on our side "scoring a point for the team". Others get upset if there's any "imbalance" between characters, or they get "upstaged" in any way.

2) The DM is overworked and doesn't have time to run a character.

With more complicated sytems (3e and 4e at higher levels), there's a good point here. The DM can design a DMPC or NPC party member, but he'll need to hand them off during play to not be distracted.

This is more true with a big group, where an NPC party member is less likely to be needed anyhow. For a tiny group (1 or 2 players), it may or may not make sense for the DM to actively run the character -- maybe role play out of combat but hand over in combat.

So back to the original question -- yes, DMPC's are a Faux Pas here, like wearing white after Labor Day. But that doesn't you can't do it and enjoy it.